When I was using Google, I'd often search "<something> emoji" which would show a result from Emojipedia where I could see and copy the emoji from the website's header. Like this:
This doesn't work with Kagi. I have to instead click the link to go to the website and then copy the emoji from the page:
It is as if Kagi removes any emojis from the header. If that's the case, this will be a problem for other websites too.
I suggest that Kagi does not strip emojis from the header, or allow an option to disable this emoji-stripping.